Computing endomorphism rings of elliptic curves under the GRH
Number Theory
2013-02-19 v2 Algebraic Geometry
Abstract
We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann hypothesis. Additionally, we improve the asymptotic complexity of previously known, heuristic, subexponential methods by describing a faster isogeny-computing routine.
Cite
@article{arxiv.1101.4323,
title = {Computing endomorphism rings of elliptic curves under the GRH},
author = {Gaetan Bisson},
journal= {arXiv preprint arXiv:1101.4323},
year = {2013}
}
Comments
11 pages, 1 figure